Time dependent solution of a queueing problem with correlated batch arrivals and general service time distribution

This paper considers the transient behaviour of queueing problem in which (i) the arrivals occur in batches of variable size (ii) the arrival and no arrival of a batch at two consecutive transition marks are correlated (iii) the service time distribution for each, unit is general with probability density functionD(x). TheLaplace transform of various probability generating functions of queue length are obtained and some particular cases are derived therefrom.     

Queues with batch poisson arrivals and hyper-exponential service time distribution

Summary We consider in this paper the transient behaviour of the queuing system in which (i) the input, following a Poisson distribution, is in batches of variable numbers; (ii) queue discipline is ‘first come first served’, it being assumed that the batches are pre-ordered for service purposes; and (iii) service time distribution is hyper-exponential withn branches. The Laplace transform of the system size distribution is determined by applying the method of generating functions, introduced in queuing theory byBailey [1]. However, assuming steady state conditions to obtain, the problem is completely solved and it is shown that by suitably defining the traffic intensity factor,ϱ, the value,p ₀, of the probability of no delay, remains the same in this case of batch arrivals also as in the case of single arrivals. The Laplace transform of the waiting time distribution is also calculated in steady state case from which the mean waiting time may be calculated. Some of the known results are derived as particular cases.     

A queueing problem with batch arrivals and correlated departures

Summary This paper considers the steady state behaviour of a queueing system in which (i) the input following the Hypergeometric Distribution is in batches of variable size (ii) queue discipline is first come first served it being assumed that the batches are preordered for service purposes and (ii) the service at two consecutive time marks is correlated. Probability generating functions for the various cases have been obtained and the mean queue lengths derived.     

Further results for the double ended queue

Summary For the double ended queue involving taxis and customers at a taxi-stand (Kashyap, 1965 a; b) the probabilities that (i) only taxis are waiting and (ii) only customers are waiting have been investigated by the use of Laplace transform. The L.T.s of the mean queue lengths of taxis and of customers are also obtained. The arrivals of taxis and customers are taken as general and Poisson respectively. The supplementary variable technique (Syski, 1960) has been used.     

Queues with hyper-poisson arrivals and bulk exponential service

Summary In this paper the time-dependent solution of a queueing system is discussed under the conditions (i) the units arrive according to Hyper-Poisson distribution withl branches (ii) the queue-discipline is ‘first come first served’ (iii) the Service-time distribution is exponential with maximum capacity ofM units being served at one instant. Some results have been obtained when the waiting space is finite; in particular the probability for service to be idle has been obtained. Also for infinite queueing-space case, the expressions for the state probabilities and the mean queuelength under steady state conditions have been found.     

ON THE DISTRIBUTIONS OF ORDER STATISTICS FOR A RANDOM SAMPLE SIZE*

The probability distribution of the i –th and j–th order statistics and of the range R of a sample of size n, taken from a population with probability density function f (x) have been obtained when the sample size n is a random variable N and has: (i) a generalized Poisson distribution; and (ii) a generalized negative bonimial distribution. Specific results are then obtained; (a) when f (x) is uniform over (0,1); and (b) when f(x) is exponential. All the results for N, being a Poisson, binomial and negative binomial rv follow as special cases.     

On the distribution of city sizes

The city size distribution in many countries is remarkably well described by a Pareto distribution. We derive conditions that standard urban models must satisfy in order to explain this regularity. We show that under general conditions urban models must have (i) a balanced growth path and (ii) a Pareto distribution for the underlying source of randomness. In particular, one of the following combinations can induce a Pareto distribution of city sizes: (i) preferences for different goods follow reflected random walks, and the elasticity of substitution between goods is 1; or (ii) total factor productivities of different goods follow reflected random walks, and increasing returns are equal across goods.     

Returns to scale in the United States intercity bus industry

This paper has taken into account the a priori restrictions available from neoclassical cost theory in evaluating the relationship between cost and the level of output and input prices for U.S. intercity bus service. A general translog cost function is used which allows tests of the degree of returns to scale, homotheticity and non-constant elasticities of substitution among input pairs. Major empirical findings are: (i) the intercity bus service can be modeled by a homothetic production function, (ii) operators can substitute labor for capital by using vehicles more extensively, (iii) there are potential economies of scale in the provision of intercity bus service, and (iv) the Cobb-Douglas functional form used in earlier studies of the industry is inappropriate.     

Using CARRX models to study factors affecting the volatilities of Asian equity markets

The range of daily asset prices is often used as a measure of volatility. Using a CARRX (conditional autoregressive range with exogenous variables) model, and the parsimony principle, the paper investigates the factors affecting the volatilities of Asian equity markets. Since the beginning of the new Century, emerging Asian markets such as Taiwan and Shanghai have been undergoing various stages of financial globalization. The volatility of the equity market may not be explained solely by its own dynamics. In this paper, we examine volatility using the following factors: (i) lagged returns; (ii) lagged absolute returns; (iii) own trading volume; (iv) U.S. factors; (v) European factors; and (vi) regional (Asian) factors. Points (i) and (iii) are by and large significant, while (ii) is not. Controlling for (i), (ii) and (iii), we find evidence that the volatility of European markets has spillovers on to both the Taiwan and Tokyo markets, mild evidence that the volatility of the U.S. market has spillovers on to the Hong Kong market, but there are no spillovers from the European or U.S. markets on to the Shanghai market.     

A queueing problem with correlated arrivals and correlated phase-type service zur theorie des rangtests

Summary This paper studies the steady-state behaviour of a discrete-time, single-channel, first-come-first-served queueing problem wherein (i) the arrivals at two consecutive time-marks are correlated (ii) the service is accomplished in phases and (iii) the completion of phases at two consecutive time-marks are correlated. The probability generating function (p.g.f.) of the number of phases waiting and in service is obtained. Further, the p.g.f. of queue length is obtained for the case when each unit demands only one phase of service, and the mean queue length is derived therefrom. Finally, the p.g.f. and the mean queue length are discussed for the special cases, (i) r=0,R≠0, (ii) r≠0,R=0, (iii) r=0,R=0, (iv) r≠0,R=−I, (v) r=0,R=−I, (vi) r=−I,R≠0, (vii) r=−I,R=0, (viii) r=I,R≠0, (ix) r=I,R=0, (x) r≠0,R=I, (xi) r=0,R=I, where r andR are the respective coefficients of correlation between arrivals and completion of phases at two consecutive time-marks.     

Voting on Pensions: A Survey

Abstract. The paper presents a nonexhaustive survey of the literature designed to explain emergence, size and political sustainability of pay‐as‐you‐go pension systems. It proposes a simple framework of analysis (a small, open, two overlapping generation economy model), around which some variants are displayed. Dictatorship of the median voter is assumed. The text is organized to answer the following questions: (i) Do political equilibria with PAYG pension schemes exist? (ii) Why do they emerge? (iii) What are the conditions for the participation constraint of the pension game to be verified?, and finally, (iv) What is the size of the pension system chosen by the median voter and how is this size influenced by an exogenous (e.g. demographic) shock?     

Scheduling spatially distributed jobs with degradation: Application to pothole repair

This paper considers scheduling spatially distributed jobs with degradation. A mixed integer programming (MIP) model is developed for the linear degradation case in which no new jobs arrive. Properties of the model are analyzed, following which three heuristics are developed, enhanced greedy, chronological decomposition and simulated annealing. Numerical tests are conducted to: (i) establish limits of the exact MIP solution, (ii) identify the best heuristic based on an analysis of performance on small problem instances for which exact solutions are known, (iii) solve large problem instances and obtain lower bounds to establish solution quality, and (iv) study the effect of three key model parameters. Findings from our computational experiments indicate that: (i) exact solutions are limited to instances with less than 14 jobs; (ii) the enhanced greedy heuristic followed by the application of the simulated annealing heuristic yields high quality solutions for large problem instances in reasonable computation time; and (iii) the factors “degradation rate” and “work hours” have a significant effect on the objective function. To demonstrate applicability of the model, a case study is presented based on a pothole repair scenario from Buffalo, New York, USA. Findings from the case study indicate that scheduling spatially dispersed jobs with degradation such as potholes requires: (i) careful consideration of the number of servers assigned, degradation rate and depot location; (ii) appropriate modeling of continuously arriving jobs; and (iii) appropriate incorporation of equity consideration.     

On interpenetrating samples of unequal sizes

Summary Koop [1967] proved that interpenetrating samples of unequal sizes are more efficient than those with equal sizes for estimating a finite population total. After observing that there is a serious lacuna present in his proof, a correct proof has been suggested. The optimum choice of individual sample sizes has also been discussed for a given (i) total sample size, (ii) cost and (iii) precision, with an assumed cost structure. Finally, the resulting estimators have been compared with those based on a single sample.     

Distributional Effects of a Continuous Treatment with an Application on Intergenerational Mobility

This paper considers the effect of a continuous treatment on the entire distribution of outcomes after adjusting for differences in the distribution of covariates across different levels of the treatment. Our methodology encompasses dose-response functions, counterfactual distributions, and ‘distributional policy effects’ depending on the assumptions invoked by the researcher. We propose a three-step estimator that consists of (i) estimating the distribution of the outcome conditional on the treatment and other covariates using quantile regression; (ii) for each value of the treatment, averaging over a counterfactual distribution of the covariates holding the treatment fixed; (iii) converting the resulting counterfactual distribution into parameters of interest that are easy to interpret. We show that our estimators converge uniformly to Gaussian processes and that the empirical bootstrap can be used to conduct uniformly valid inference across a range of values of the treatment. We use our method to study intergenerational income mobility where we consider effects of parents’ income on features of their child's income distribution such as (i) the fraction of children with income below the poverty line; (ii) the variance of child's income; and (iii) the inter-quantile range of child's income–all as a function of parents’ income.     

Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics

This paper studies taper-based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework, and makes several theoretical contributions: (i) we treat multiple frequencies jointly, (ii) we allow for long-range dependence or anti-persistence at differing frequencies, (iii) we allow for tapers that are only piecewise smooth or discontinuous, including flat-top and truncation tapers, (iv) we study higher-order accuracy through the limit distribution’s Laplace Transform, (v) we develop a taper-based estimation theory for the spectral distribution, and show how confidence bands can be constructed. Simulation results produce quantiles and document the finite-sample size properties of the estimators, and a few empirical applications demonstrate the utility of the new methods.     

IPO mechanism selection by using Classification and Regression Trees

The Turkish IPO market gives issuers and underwriters a choice of three different IPO selling mechanisms. The current paper sheds new light on the determinants of these issue procedures within the context of the following methods (i) book building mechanism, (ii) fixed price offer, and (iii) sale through the stock exchange. Most of the empirical models in the IPO literature use binary probit and logit models to determine the factors behind the choice of one method over another and try to answer the question of “why is such a mechanism chosen”. To understand the reasons on issuers’ selection of IPO mechanism, we have conducted a Classification and Regression Trees (CART) methodology to represent decision rules in a form of binary trees. Our results indicate that, CART methodology predicts a firms’ IPO selling mechanism with 77.42% accuracy. The most important variable that determines the IPO selling mechanism is the Arrangement Type between the issuer and the underwriter as in the form of best effort and firm-commitment.     

An axiomatization of the core of cooperative games without side payments

Let M be a set of m players, m≧3, and let Γ be the set of all (finite) games (without side payments) that have a non-empty core. When M is finite, the following four (independent) axioms fully characterize the core on Γ: (i) non-emptiness, (ii) individual rationality, (iii) the reduced game property, and (iv) the converse reduced game property. If M is infinite, then the converse reduced game property is redundant.     

On theE-optimality of certain asymmetrical designs under mixed effects model

TheE-optimality of the following designs within the class of all proper and connected designs with givenb, k andv under mixed effects model are established.

1. A group divisible design with λ₂ = λ₁ + 1.
2. A group divisible design with λ₁ = λ₂ + 1 and group size 2.
3. A linked block design.
4. The dual of design (i)
5. The dual of design (ii).

All these designs are known to satisfy the same optimality property under fixed effects model whenk<v, while the design (i) is known to beE-optimal even whenk>v. From the results proved here, theE-optimality of designs (ii, (iii), (iv) and (v) under fixed effects model in the situation whenk >v also follows.     

Global team members’ performance and the roles of cross-cultural training,cultural intelligence,and contact intensity: the case of global teams in IT offshoring sector

Abstract

This study investigates an unexplored form of global team prevalent in the Information Technology (IT) offshoring sector where IT service providers work alongside with client representatives in a global team context. Guided by theories of intelligence and intergroup contact, this study investigates global team members’ individual-level task performance. Specifically, this study examines the development of global team members’ cultural intelligence (CQ) following cross-cultural training. This study also determines the effects of improved CQ on individual-level task performance and examines the moderating role of contact intensity on the relationship between improved CQ and individual-level task performance. Data on the development of CQ, participation in cross-cultural training, and contact intensity were collected from 225 global team members while data on task performance were obtained from each of the global team members’ supervisors. The results of the statistical analyses reveal that: (i) CQ improved following participation in cross-cultural training sessions; (ii) improved CQ is positively and significantly related to individual-level task performance; and (iii) contact intensity moderates the relationship between improved CQ and individual-level task performance. These findings have a number of theoretical and practical implications for international organizations such as those in the IT offshoring sector.     

Dynamic factor model with infinite‐dimensional factor space: Forecasting

The paper compares the pseudo real‐time forecasting performance of three dynamic factor models: (i) the standard principal component model introduced by Stock and Watson in 2002; (ii) the model based on generalized principal components, introduced by Forni, Hallin, Lippi, and Reichlin in 2005; (iii) the model recently proposed by Forni, Hallin, Lippi, and Zaffaroni in 2015. We employ a large monthly dataset of macroeconomic and financial time series for the US economy, which includes the Great Moderation, the Great Recession and the subsequent recovery (an update of the so‐called Stock and Watson dataset). Using a rolling window for estimation and prediction, we find that model (iii) significantly outperforms models (i) and (ii) in the Great Moderation period for both industrial production and inflation, and that model (iii) is also the best method for inflation over the full sample. However, model (iii) is outperformed by models (ii) and (i) over the full sample for industrial production.